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future and participle contructions

Could you please explain the difference between 'future tense and future progressive tense?'

#1 I will do it.

#2 I will be doing it.

Participle Contruction

Are the following sentences interchangeable/ do they have the same meaning?

#1 Arriving at the hotel, they began to quarrel. And
#2 Having arrived at the hotel, they began to quarrel.

To my best knowledge, they can be interchanged. Is that correct?

Now here is the devil sentence which is trying to confuse me;

'Watching TV, he did his homework' should mean that the person did them at the same time, according to a grammer book I read recently. If the book's explanation might be correct, the above sentences should be incorrect that they can interchangeable
Could you please help me get out of this confusion?

'Having watched TV, he did his homework' should mean that the person did that watching TV, then he started to do his homework. That is in my book correct. What about yours?

I sometimes have some pb with these 2 tenses too. I don't think they're always interchangeable though.
Eg.
"In exactly two days I will be sunbathing on the beach" (I'll be doing it at that time =&gt; progressive aspect)
"In two days I will set off to Hawaii" (no progressive aspect)

'Watching TV, he did his homework' should mean that the person did them at the same time, according to a grammer book I read recently. If the book's explanation might be correct, the above sentences should be incorrect that they can interchangeable
Could you please help me get out of this confusion?

Well, I agree with the book. We could rephrase it: "he did his homework while watching TV" (sounds even more natural to me).

'Having watched TV, he did his homework' should mean that the person did that watching TV, then he started to do his homework. That is in my book correct. What about yours?

Correct. First he watched TV, then he did his homework. Two consecutive actions.